As is known in the art, when storing data in a data storage system it is common to “code” the “raw”, original user data in some way so as to, for example, make the data storage more efficient, and less susceptible to errors. There are typically three types of coding that are employed when storing data on a storage medium.
Firstly, the original data would normally be compressed in some way. This is commonly referred to as source coding. The next stage is usually to encode the compressed data to provide some form of error protection. This usually involves a coding process that adds a few bytes to the data, which bytes can then be used to detect and correct errors when the data is read out. A common example of such error correction coding (ECC) is Reed-Solomon coding.
The error correction coded data is then typically subject to further encoding, which further encoding is usually referred to as “modulation coding.” This coding is used to impose constraints on the data sequences written on to the storage medium (e.g., such that there can be no more than three consecutive “0”s) and is done for “house-keeping” purposes, e.g., to aid timing recovery and gain control and to shorten the detector path memory. Modulation coding can also improve performance of the storage system (an example of this is the use of (d, k) codes in magnetic and optical storage systems).
After modulation coding, the data may then be further “parity” coded, as is known in the art, to add one or more parity bits to the data. Thereafter the data can be written to the storage medium, e.g. magnetic tape or disk drive, or optical disk, and stored.
Reading the data from the storage medium and restoring the original data is the reverse process. Thus, for example, the detector output read from the storage medium is fed to a post-processor that performs soft-decision decoding of the parity-check code, a modulation decoder is then used to invert the modulation coding, and finally an error detection decoder is used to correct errors and deliver (its estimate of) the (compressed) original user data.
As is known in the art, the modulation coding step discussed above usually involves two steps. The first is so-called modulation coding that maps bits in the input data stream to a particular constrained output bit arrangement; for example a 16/17 code mapping a 16 bit input to a constrained 17 bit output data sequence. Examples of such modulation coding are constrained codes such as so-called run length limited (d, k) constrained codes, (G, I) constrained codes, and maximum transition run (j, k) constrained codes. Hereinafter, the term “modulation coding” will be used to refer to the application of this form of constrained coding, excluding any subsequent precoding step (see below).
The second step in the overall “modulation” coding process is so-called “precoding”. Precoding operates on the “constrained” coded data and operates, as is known in the art, effectively to convert or translate a more simple set of constraints that are imposed on a data sequence by modulation (constrained) coding into a larger and more complex set of constraints that it is actually desired to impose on the data sequence, e.g., at the channel input. For example, with reference to the above discussed coding “constraint” of there being no more than three “0”s in succession, the use of precoding can “translate” that relatively simple constraint into the twin requirements that there can be no more than four “0”s in succession and that there can be no more than four “1”s in succession. For a given encoder and decoder structure, such as a block encoder and block decoder, precoding may allow stronger constraints to be imposed on the data sequence but without the need for a commensurate increase in the complexity of the modulation coding that is applied. Thus using precoding simplifies the modulation coding that needs to be performed. Examples of precoding techniques that are used are so-called 1/(1⊕D2) and 1/(1⊕D) precoding, as is known in the art (where ⊕ indicates the Boolean logic operation XOR (exclusive OR)).
As is known in the art, the overall aim of modulation coding and precoding is to adapt the data signal to the (recording) channel that it is subsequently to be “transmitted” on. A more general discussion of coding, including modulation coding and precoding, can be found, e.g., in K. A. S. Immink, P. H. Siegel, and J. K. Wolf, “Codes for Digital Recorders”, IEEE Trans. Inform. Theory, Vol. 44, pp 2260-2299, October 1998.
However, a disadvantage to the use of precoding is that it can introduce error propagation and increase errors when the stored data is read out. This is because, as is known in the art, in the inverse precoding step each single read stored bit is usually used to determine two output bits of the inverse precoding process. Thus an error in a single stored bit can result in two bit errors in the output from the inverse precoder. This can then lead to further error propagation in modulation decoding and degrade error correction performance.